
\def\ttb{t\overline{t}}
\def\Zbb{Z\rightarrow b\overline{b}}
\def\WHqb{WH\rightarrow q\overline{q'} b\overline{b}}
\def\ZHqb{ZH\rightarrow q\overline{q} b\overline{b}}

%% Misc.

\def\insertfig#1{
  \openin 1 #1
  \ifeof 1
    \closein 1
    \typeout{File #1 does not exist} \vskip 1truecm 
    \centerline{\fbox{Missing: #1}} \vskip 1truecm
  \else
    \closein 1
    \typeout{Reading figure in #1}
    \leavevmode\epsfxsize=\textwidth\epsfbox{#1}
  \fi
}
\def\OOO{\hphantom{O}}


The first of these sections describes the data samples and
normalizations used in the analysis.  The second describes the
selection criteria, and the third describes the relationship between
the analysis sensitivity and hypothetical improvements in event
reconstruction.  The last section contains the conclusions.

\newpage
\vspace{0.2in}
{\bf Event Samples} \\ \nopagebreak

For the channels considered here, the dominant background is QCD
production of four jet events, two of which are $b$-quark jets.
Other backgrounds include $\ttb$ and single-$t$ events, $WZ$ events,
$WW$ events, $W+2$~jet events and $Z+2$~jet events.  The relative
cross sections after a basic four-jet selection are given in
Table~\ref{t-bkg-xsec}.  One sees that the QCD multijet events
completely dominate the other backgrounds.  The multijet cross section
in Table~\ref{t-bkg-xsec} was computed by multiplying the total
four-jet cross section observed in a monitor data sample (described
below) by the fraction of simulated four-jet events which have two or
more $b$-quark jets.  The $\ttb$ cross section uses the D\O\
published value. The remaining cross-sections are purely theoretical
and were taken from either CompHep($W+\bb$) or Pythia(all others).
The QCD multijet background is roughly five orders of magnitude larger
than all others.  Because of this, the background calculations are
made using only QCD production.  All others are neglected.

\def\9{\hphantom{0}}
\begin{table}
\caption{$WH\rightarrow jj\bb$, SHW analysis.
 The total cross section times branching ratio to hadronic final
 states and accepted cross section times branching ratio for a basic four jet
 selection for background events.  One sees that the QCD multi-jet background
 is roughly five orders of magnitude larger than all others.   Only the QCD
 background is considered in the remainder of this analysis.\label{t-bkg-xsec} }
\begin{center}
\begin{tabular}{|l||c|c|} %\hline
\noalign{\vskip-6pt}
   & \multicolumn{2}{c|}{Cross Section (fb)} \\
 Sample & Total & 4-jet Accepted \\ \tableline
Multijet   & --- & $\approx10^8$ \\
 $\ttb$    &  2600  & 2600 \\
 $WW$      &  4000  & 2700 \\
 $WZ$      &  1400  & \9900 \\
 $ZZ$      & \9490  & \9350 \\
 $W+\bb$   &   ---  & 2000
%\hline
\end{tabular}
%\caption{$WH\rightarrow jj\bb$, SHW analysis.
% The total cross section times branching ratio to hadronic final
% states and accepted cross section times branching ratio for a basic four jet
% selection for background events.  One sees that the QCD multi-jet background
% is roughly five orders of magnitude larger than all others.   Only the QCD
% background is considered in the remainder of this analysis.\label{t-bkg-xsec}}
\end{center}
\end{table}


Run 1 monitor data taken with the D\O\ detector were used to provide the jet
rapidity and momentum distributions for the multijet background.  The sample
represented approximately 1~nb$^{-1}$ of exposure and events were required to
have passed a trigger of at least one L1 trigger tower with $\et\ge 5$~GeV and
at least three L2 trigger jets with $\et\ge 15$~GeV.  In addition standard
quality requirements were made.  The triggered sample contained approximately
$10^5$ events.  The flavor information of each jet in an event was randomly
assigned according to the flavor-by-jet-rank distributions from Pythia+SHW.


Signal samples of $WH$ events were generated using Pythia.  The $W$ boson was
forced to decay to quarks and the Higgs was required to decay to $\bb$.  The
quark flavors in the vector boson decay were distributed according to the
standard model expectation.  The Pythia four-vectors were then input to SHW
for detector simulation.  Samples were generated for Higgs masses of 80, 90,
100, 110, 120, 130 and 140~GeV.


The $ZH$ final states were not directly simulated.  Instead, it was assumed
that the acceptance and distributions were identical to those for the $WH$
modes.  The $W$ mass, $WH$ production cross section, and $W \rightarrow
q\bar{q^{\prime}}$ branching ratio, had of course been replaced by the
corresponding quantities for the $Z$ boson.  Thus, we report results for
inclusive production of $WH$ and $ZH$.

\begin{table}
\caption{$WH\rightarrow jj\bb$, SHW analysis.
         The acceptance as a function of Higgs mass for 
         the basic four-jet selection in the $WH$ channel.}
\label{t-sig-xsec}
\begin{center}
\begin{tabular}{cc} %\hline
 $m_H$ (GeV) & Acceptance\\ \tableline
 \hphantom{1}80 &  0.11 \\
 \hphantom{1}90 &  0.13 \\
            100 &  0.14 \\
            110 &  0.15 \\
            120 &  0.16 \\
            130 &  0.15 \\
            140 &  0.13 
%\hline
\end{tabular}
%\caption{$WH\rightarrow jj\bb$, SHW analysis.
%         The acceptance as a function of Higgs mass for 
%         the basic four-jet selection in the $WH$ channel.}
%\label{t-sig-xsec}
\end{center}
\end{table}


\vspace{0.2in}
{\bf Selection Criteria} \\ \nopagebreak

The analysis selection is quite simple.   The requirements are:
\begin{itemize}
  \item $N_{jet}\ge 4$ 
  \item $N_b\ge 2$
  \item $|\Delta\eta_{\bb}|\le 1,\ |\Delta\eta_{jj}|\le 1$
  \item $M_{jj} \ge M_W - \sigma(M_{jj})$\footnote{For the $ZH$ modes, $M_W$ 
    was replaced by $M_Z$.}
  \item $M_{\bb} \ge m_H - \sigma(M_{\bb})$.
\end{itemize}
Here $N_J$ is the number of $\Delta R =0.5$ cone jets in the event
which satisfy $|\eta|\le2.0$ and $p_T\ge15$~GeV.  $N_b$ is the number
of 0.5 cone jets tagged as $b$-quark jets using the SHW $b$-tag
algorithm based on a displaced vertex or a soft lepton.\footnote{This
is a parameterization based on true jet flavor and $p_T$.  It includes
mistag parameterizations for light quarks and $c$-quarks.}  Tag jets
must also satisfy $|\eta|\le2.0$ and $p_T\ge15.0$.  The variables
$\Delta\eta_{\bb}$ and $\Delta\eta_{jj}$ are the difference in
pseudorapidity $\eta$ between the two $b$-tagged jets
($\Delta\eta_{\bb}$) and the two non-tagged jets($\Delta\eta_{jj}$).
The masses $M_{\bb}$ and $M_{jj}$ are respectively the masses of the
$b$-tagged jet pair and the non $b$-tagged jet pair in the event.
For properly assigned flavors, these masses should be close to the
Higgs mass $m_H$ and the $W$ mass $M_W$.  The resolution parameters
$\sigma(M_{\bb})$ and $\sigma(M_{jj})$ are, respectively, the RMS
values of the mass distributions for the Higgs and $W$ decay products
seen in simulated events.

% (see Fig.~\ref{f-mbb} and \ref{f-mjj} in the following).


Other simple variables (including the $p_T$ of the $b\bar{b}$ system,
total energy and scalar $H_T$ of the four jets, rapidity boost of the
$b\bar{b}$ and $jj$ systems) have been investigated and found not to
contribute significantly beyond these.  The $\Delta\eta$ requirements
arise because the signal is peaked toward narrower opening angles
than the background.  This arises because the $W$ and Higgs are
boosted, so their decay products will on average be closer together
than any given jet pair from the four jets in multijet backgrounds.


The $WH$($ZH$) events should show peaks in the reconstructed dijet
mass spectra near the $W(Z)$ mass for non $b$-tagged jets and near
the Higgs mass for the $b$-tagged jets.  The multijet background, on
the other hand, should have no such peaks, but instead be a steeply
falling distribution in both masses.  This observation motivates the
last two requirements which simply demand that the reconstructed
masses lie near the $W$($Z$) and Higgs masses.  The distributions are
shown in two-dimensional plots, for $m_H=100$ GeV, in
Figure~\ref{f-mbkg-msig}.  In all figures, the background corresponds
to a luminosity of 1 pb$^{-1}$, while the signal plots correspond to
30.5~fb$^{-1}$.


\begin{figure}
  \begin{center}
    \parbox{6.0in}{\epsfxsize=\hsize\epsffile{whjj/mjj_mbb_100_bw.eps}}
  \end{center}
  \caption{$WH\rightarrow jj\bb$, SHW analysis.
           $M_{jj}$ vs. $M_{\bb}$ for the multijet background sample
          (left histogram) and the $WH$ signal (right histogram).
          The background events represent 1 pb$^{-1}$ of integrated
          luminosity. The signal events correspond to 30.5 fb$^{-1}$.
          The dashed lines represent the applied selection criteria 
          on $M_{\bb}$ and $M_{jj}$ for a 100~GeV Higgs.} 
  \label{f-mbkg-msig}
\end{figure}


A number of different ways of imposing the mass condition were
considered.  In addition to the final choice of lower bounds on
$M_{\bb}$ and $M_{jj}$, elliptical regions centered around the masses
and diagonal lines were also considered.  In the absence of
backgrounds other than multijet production, the various methods gave
similar results, so the simple box was chosen.  If additional
backgrounds, particularly top production, would be added, a
requirement which also places an upper bound on the reconstructed
masses might also be needed.

The effects of the selection cuts on the background and signal samples
are shown in Table~\ref{t-effi} as number of events corresponding to
an integrated luminosity of 1 fb$^{-1}$.

\begin{table}
\caption{Number of events corresponding to 1 fb$^{-1}$ integrated
         luminosity, for $WH+ZH$ signal (S) and multijet background (B).
         Basic Jet selection includes the requirements
         on jet multiplicities, jet $E_T$'s and $\eta$'s.\label{t-effi}}
\begin{center}
\begin{tabular}{|c||r|c||r|c||r||c|c|} %\hline
\noalign{\vskip-6pt}
                & \multicolumn{2}{c||}{Basic Jet Selection}
                & \multicolumn{2}{c||}
                 {$\Delta\eta_{\bb}$, $\Delta\eta_{jj}$ Selection}
                & \multicolumn{3}{c|}{Mass Cut} \\ \hline
  $m_H$ (GeV)   & $S\;\;\;$ & $B\;\;\;\;\,$ 
                & $S\;\;\;$ & $B\;\;\;\;\:$ 
                & $S\;\;\;$ & $B\;\;\;\;\:$ & $S/\sqrt{B}$ \\ \hline\hline 
\hphantom{1}80 & 58 & 860000 &27 & 200000 & 11    & 6800 & 0.13 \\
\hphantom{1}90 & 48 &   ''   &23 &   ''   &  8.1  & 5400 & 0.11 \\
           100 & 38 &   ''   &17 &   ''   &  5.6  & 3600 & 0.09 \\
           110 & 28 &   ''   &12 &   ''   &  3.5  & 2800 & 0.07 \\
           120 & 19 &   ''   & 8 &   ''   &  2.5  & 2300 & 0.05 \\
           130 & 10 &   ''   & 5 &   ''   &  1.3  & 2000 & 0.03 \\
           140 &  4 &   ''   & 2 &   ''   &  0.45 & 1700 & 0.01 \\
\hline
\end{tabular}
%\caption{Number of events corresponding to 1 fb$^{-1}$ integrated
%         luminosity, for $WH+ZH$ signal (S) and multijet background (B).
%         Basic Jet selection includes the requirements
%         on jet multiplicities, jet $E_T$'s and $\eta$'s.\label{t-effi}}
\end{center}
\end{table}


The data in Table~\ref{t-effi} were used to derive luminosity
requirements to achieve 95\% C.L. exclusion limits, and $3\sigma$ and
$5\sigma$ excesses.  The significance $s$ is defined as $s\equiv
S/\sqrt{B}$.  Here $S$ is the number of signal events for a given
luminosity, and $B$ is the number of background events in the same
luminosity.  This measure of significance corresponds to the
probability that the background fluctuates upward to at least the
number of observed signal events.  In all cases, one-sided, gaussian
confidence intervals were used.  The results are shown in
Figure~\ref{f-answ1} plotted as luminosity required versus Higgs mass.

\begin{figure}
  \begin{center}
    \parbox{4.0in}{\epsfxsize=\hsize\epsffile{whjj/plot_1_bw.eps}}
  \end{center}
  \caption{Luminosity required to achieve a given signal significance versus
           Higgs mass.}
  \label{f-answ1}
\end{figure}

\vspace{0.2in}
{\bf Improvements} \\ \nopagebreak

There are a number of ways in which this analysis could be improved.  Among
them are:
\begin{enumerate}
  \item the reconstructed mass resolution is improved relative to the SHW
    results,
  \item the $b$-quark jet identification efficiency or purity is improved and
  \item other analysis techniques, particularly multivariate likelihoods or
    neural nets, giving significantly improved background rejection or signal
    acceptance.
\end{enumerate}
We have attempted to assess the improvements these might offer by
computing the luminosity required to reach a given statistical
significance for a hypothetical improvement in discrimination were
made.


The most likely candidate is improved $\bb$ mass resolution.  The
current jet finding algorithm uses only calorimeter information.  It
has already been shown that including additional information will
improve the reconstructed mass.  Also, the jet corrections used in
this analysis were designed only to correctly reproduce the peak
positions of the mass distributions.  No attempt was made to minimize
the resolution.  Figure~\ref{f-mbb-plus} shows the significance versus
mass resolution for $m_H=100$~GeV and 1~fb$^{-1}$.  This result was
derived by improving the signal mass resolution $\sigma$ by a fixed
amount and making the same box selection as the standard analysis.
Because $\sigma$ is smaller, the selection requirement,
$M_{jj}\geq M_W-\sigma$, corresponds to a higher minimum mass.  Thus,
this procedure corresponds to a fixed acceptance (for the signal) and
decreasing background.  One sees that a factor of two improvement in
mass resolution corresponds to a factor of four reduction in
background and thus a factor of two improvement in significance.

\begin{figure}
  \begin{center}
    \parbox{3.0in}{\epsfxsize=\hsize\epsfbox{whjj/plot_2_bw.eps}}
    \parbox{3.0in}{\epsfxsize=\hsize\epsfbox{whjj/plot_3_bw.eps}}
  \end{center}
  \caption{Signal significance as a function of mass resolution (left-hand
            panel) and as a function of second-jet tag probability (right-hand panel).
            The standard SHW processing gives $\delta M/M\approx 20$\% for the 
            four-jet final states considered here.}
\label{f-mbb-plus}
\end{figure}

It is also possible that as the Run 2 data are processed, we will be
able to increase the $b$-tagging efficiency or purity.
Figure~\ref{f-mbb-plus} also shows the significance as a function of
tagging efficiency of the second $b$-tagged jet.  The improvement is
realized by multiplying the standard SHW tag probability for the
second jet by the factor shown on the abscissa with the constraint
that the efficiency never exceed unity.  One sees that a 50\%
improvement in efficiency gives only a modest gain in significance.


